Geoscientific Model Development Open Access Hydrology and Earth System Sciences Open Access Geosci Model Dev., 6, 1591–1599, 2013 www.geosci-model-dev.net/6/1591/2013/ doi:10.5194/gmd-6-1591-2013 © Author(s) 2013 CC Attribution 3.0 License ess Data Systems Ocean Science H Yan1,2 , Z Wang1 , and J Li2 Open Access An approach to computing direction relations between separated object groups Department Open Access of Geographic Information Science, Faculty of Geomatics, Lanzhou Jiaotong University, Lanzhou 730070, China Department of Geography & Environmental Management, Faculty of Environment, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada Solid Earth Correspondence to: H Yan (h24yan@uwaterloo.ca) The Cryosphere Abstract Direction relations between object groups play an important role in qualitative spatial reasoning, spatial computation and spatial recognition However, none of existing models can be used to compute direction relations between object groups To fill this gap, an approach to computing direction relations between separated object groups is proposed in this paper, which is theoretically based on gestalt principles and the idea of multi-directions The approach firstly triangulates the two object groups, and then it constructs the Voronoi diagram between the two groups using the triangular network After this, the normal of each Voronoi edge is calculated, and the quantitative expression of the direction relations is constructed Finally, the quantitative direction relations are transformed into qualitative ones The psychological experiments show that the proposed approach can obtain direction relations both between two single objects and between two object groups, and the results are correct from the point of view of spatial cognition Introduction Direction relation, along with topological relation (Egenhofer and Franzosa, 1991; Roy and Stell, 2001; Li et al., 2002; Schneider and Behr, 2006), distance relation (Liu and Chen, 2003), and similarity relation (Yan, 2010), has gained increasing attention in the communities of geographic information sciences, cartography, spatial cognition, and various location-based services (Cicerone and De Felice, 2004) for years Its functions in spatial database construction (Kim Open Access Received: 23 April 2013 – Published in Geosci Model Dev Discuss.: June 2013 Revised: August 2013 – Accepted: 14 August 2013 – Published: 17 September 2013 and Um, 1999), qualitative spatial reasoning (Frank, 1996; Sharma, 1996; Clementini et al., 1997; Mitra, 2002; Wolter and Lee, 2010; Mossakowski, 2012), spatial computation (Ligozat, 1998; Bansal, 2011) and spatial retrieval (Papadias and Theodoridis, 1997; Hudelot et al., 2008) have attracted researchers’ interest Direction relation has also been used in many practical fields (Zimmermann and Freksa, 1996; Kuo et al., 2009), such as combat operations (direction relation helps soldiers to identify, locate, and predict the location of enemies), driving (direction relation helps drivers to avoid other vehicles), and aircraft piloting (direction relation assists pilots to avoid terrain, other aircrafts and environmental obstacles) A number of models for describing and/or computing direction relations have been proposed, including the conebased model (Peuquet and Zhan, 1987; Abdelmoty and Williams, 1994; Shekhar and Liu, 1998), the 2-D projection model (Frank, 1992; Nabil et al., 1995; Safar and Shahabi, 1999), the direction-relation matrix model (Goyal, 2000), and the Voronoi-based model (Yan et al., 2006) These models can compute direction relations between two single objects, but can not compute direction relations between two object groups Nevertheless, objects on maps may be viewed as groups in many cases in light of gestalt principles, such as proximity, similarity, common orientation/direction, connectedness, closure, and common region (Palmer, 1992; Weibel, 1996; Yan et al., 2008) In other words, objects close to each other, with similar shape and/or size, arranged in a similar direction, topologically and/or visually connected, with a closed tendency, and/or in the same region have Published by Copernicus Publications on behalf of the European Geosciences Union M 1592 H Yan et al.: An approach to computing direction relations between separated object groups (a) (b) (c) (d) (e) (f) Explanation: the objects enclosed by dash-lined rectangle are viewed as a group – The cone-based model (Peuquet and Zhan, 1987) partitions the 2-dimensional space around the centroid of the reference object into four direction regions corresponding to the four cardinal directions (i.e., N, E, S, W) The direction of the target object with respect to the reference object is determined by the target object’s presence in a direction partition for the reference object If the target object coincides with the reference object, the direction between them is called “same” a This model is developed primarily to detect whether a target object exists in a given direction or not If the distance between the two objects is much larger than their Fig.1 Objects on on maps as aa group groupininlight light Fig Objects mapsare areviewed viewed as of of thethe Gestalt size, the model works well; otherwise a special method gestalt principles: (a) proximity; (b) similarity; (c) similar direcprinciples: (a)proximity; (b)similarity; (c)similar direction; must be used to adjust the area of acceptance If objects tion; (d) connectedness; (e) closed tendency; and (f) same region (d)connectedness; (e)closed tendency; and (f)same region are overlapping, intertwined, or horseshoe-shaped, this model uses centroids to determine directions (Peuquet and Zhan, 1987), and the results are misleading somea tendency to be viewed as a group (Fig 1) Four catetimes In addition, if a target object is in multiple direcgories of object groups can be differentiated according to tions, such as {N, NE, E}, this model does not provide the geometric ingredients of the single objects: point, linear, a knowledge structure to represent multiple directions areal/polygonal, and complex object groups Figure shows (Goyal, 2000) a number of pairs of object groups Thus, it is of great importance to find methods to obtain direction relations between – The 2-D projection model (Frank, 1992; Nabil et al., object groups 1995; Safar and Shahabi, 1999) represents spatial relaBecause none of the models for computing direction retions between objects using MBRs (minimum bounding lations between object groups has been proposed, this paper rectangles) Reasoning between projections of MBRs will focus on filling this gap After the introduction (Sect 1), on the x and y axes is performed using 1-D interval existing models for computing direction relations will be disrelations Using this method, one can characterize relacussed (Sect 2) Then the theoretical foundations of the new tions between MBRs of objects uniquely There are 13 approach will be presented (Sect 3), and a Voronoi-based possible relations on an axis (Allen, 1983; Nabil et al., model for computing directions between object groups will 1995) in 1-D space; therefore, this model distinguishes be proposed (Sect 4) After that, a number of experiments 13 × 13 = 169 relations in 2-D space will be shown to demonstrate the validity of the proposed approach (Sect 5) Finally, some conclusions will be made The 2-D projection model approximates objects by their (Sect 6) MBRs; therefore, the spatial relation may not necessarily be the same as the relation between exact representations of the objects, because the model can not capture Analysis of existing models the details of objects in direction descriptions (Goyal, 2000) So this model can be only used for the qualitaTo propose a model for computing direction relations betive description of direction relations tween object groups, it is pertinent to summarize and analyze previously existing ones to show their advantages and disadvantages – The direction-relation matrix model (Goyal, 2000) parTo facilitate the discussion in the following sections, it is titions space around the MBR of the reference object designated that into nine direction tilts: N, NE, E, SE, S, SW, W, NW, and O (same direction) A direction-relation matrix is A is the reference object (or object group), and B is the constructed to record if a section of the target object target object (or object group); falls into a specific tilt Further, to improve the reliability of the model, a detailed direction-relation matrix Dir(A, B) is the qualitative description of direction recapturing more details by recording the area ratio of the lations from A to B; target object in each tilt is employed D(A, B) is the quantitative description of direction reThe direction-relation matrix model provides a knowl27 lations from A to B ; and edge structure to record multilevel directions How4 only extrinsic reference frame is employed for direction ever, it can not obtain D(A, B)/Dir(A, B) from relations D(B, A)/Dir(B, A)and vice versa (Yan et al., 2006) Geosci Model Dev., 6, 1591–1599, 2013 www.geosci-model-dev.net/6/1591/2013/ Roads Shops (b) 10 Roads 11 12Village 13boundary 14 (d) 15 H Yan et al.: An approach to computing direction relations between separated object groups Village A Village B (a) Land Archipelag o (c) Green land River basin Lakes (f) Village River (g) B Fig Principle of the Voronoi-based model used to describemodel direcFig.3 Principle of the Voronoi-based tion relations between single objects used to describe direction relations between single objects simplicity: computation of the direction relations between arbitrary two objects is not time-consuming, and the model is easy to be understood; inversion: Dir(B, A)/D(B, A) can be obtained by Dir(A, B)/D(A, B); correctness: results obtained are consistent with human’s spatial cognition; qualification: the model can give qualitative representations of direction relations Village Village Voronoi edges quantification: the model can give quantitative representations of direction relations; and Lakes (e) A 1593 Table shows the advantages and disadvantages of the above models Obviously, none of the existing models meets the five criteria And, particularly, none of them can be used to compute direction relations between object groups (h) Theoretical foundations of multi-directions Fig.2 Examples of various pairs of object groups: (a) Fig Examples of various pairs of object groups: (a) points– Direction relations between object groups need to be depoints-points; (b) points-lines; (c) points-polygons; points; (b) points–lines; (c) points–polygons; (d) lines–lines; (e) (d) scribed using multiple directions in many cases The exlines-lines; (e) (f)lines-polygons; (f) (g)polygons-polygons; lines–polygons; polygons–polygons; line–complex; and (h) (g) amples of multiple directions are very common in the geline-complex; and (h) complex-complex complex–complex ographic space Especially if two object groups are intertwined, enclosed, or overlapping with each other, description of direction relations with multiple directions becomes un– The Voronoi-based model (Yan et al., 2006) uses “diavoidable rection group” because people describe directions between two objects using multiple directions A direction group consists of multiple directions, and each direction includes two components: the azimuths of the normals of direction Voronoi edges between two objects and the corresponding weights of the azimuths (Fig 3) 28 The Voronoi-based model can describe direction relations quantitatively and qualitatively, and can obtain D(B, A) by D(A, B) Direction relations are recorded in 2-dimensional tables The above four models may be compared using the following five criteria (Goyal, 2000; Yan et al., 2006) www.geosci-model-dev.net/6/1591/2013/ 3.1 Examples of multi-directions – Example 1: UniRoad composed of three roads passes through University A composed of many buildings (Fig 4) The direction relations between the road and the university can not be simply described by a single cardinal direction – Example 2: as a very common case, a road runs approximately parallel with a river In Fig 5, a man may say “the road is to the northeast of the river” when he is at P ; and he may say “the road is to the north of the river” Geosci Model Dev., 6, 1591–1599, 2013 1594 H Yan et al.: An approach to computing direction relations between separated object groups Table Comparison of the existing models Models Simplicity Inversion Correctness Qualification Quantification Cone-based model 2-D projection model Direction-relation matrix model Voronoi-based model Yes Yes Yes No Yes Yes No Yes Not always Not always Not always Yes Yes Yes Yes Yes No No Yes Yes University A UniRoad River basin R UniRoad Un University A iR oa Village V Fig.4 Multi-directions are needed Fig.object If an object group is half-enclosed by another group, group is half-enclosed bya single another gr when two object groupsFig.6 are If an direction is not enough to describe their direction relations intertwined a single direction is not enough to describe their direc Fig Multi-directions are needed when two object groups are intertwined d relations P River A the principle of gestalt It is the perception of a composition as a whole Human’s perception of the piece is based on their understanding of all the bits and pieces working in unison People usually ignore the trivial of spatial objects but get the sketches of the whole before they judge directions Their judgments are based on the sketches but not on details This process implies the idea of cartographic generalization The generalization methods in direction judgments are a little bit different from those used in traditional map generalization (Weibel, 1996) The generalization scale depends on the size of the field formed by the two object groups The larger the distance between the two groups, the larger the objects are generalized Road B Q R Fig.5Fig Multi-directions Multi-directions between two between two approximately parallel object groups approximately parallel object groups when he is at Q; however, if he walks to R, he may say: “the road is to the east of the river” Nevertheless, all three answers are intuitively partial and unacceptable To give a whole description, it is reasonable to combine the three answers – Example 3: in Fig 6, village A (a group of buildings) is half-enclosed by river R (a group of river branches) A single cardinal direction obtained by the cone-based model (e.g., A is at the south of R) can not describe their direction relations clearly – Proximity: the principle of proximity or contiguity states that nearby objects can be regarded as a group and more correlated (Alberto and Charles, 2011) Such examples exist almost everywhere in daily life In Fig 6, the three directions are obtained by the three pairs of proximal sections of the road and the river Hence, “judging directions by proximal sections” will be one of the most important principles in the new model 3.2 Cognitive explanation of multi-directions 3.3 From the point of view of perception, in any case, the following two principles remain unquestionable in direction judgments In our daily life, when a man says “the hospital is to the east of the school”, he generally has an imaginary ray (here, ray is directly borrowed from its mathematical concept) in his brain, pointing from the hospital to the school indicating the direction Hence, it is a natural thought to express direction relations using such rays If multi-directions exist between two object groups, a combination of multiple rays – Relations between the sum of the whole and its parts: “the sum of the whole is greater than its parts” (Wertheimer, 1923; Clifford, 2002) is the idea behind Geosci Model Dev., 6, 1591–1599, 2013 Expression of multi-directions www.geosci-model-dev.net/6/1591/2013/ H Yan et al.: An approach to computing direction relations between separated object groups A 1595 River basin R L Ray Village V B (a) A (b) Voronoi edge (b) (a) Legend Voronoi edges Fig.7 Normals of the Voronoi edges used to denote directions Fig Normals of the Voronoi edges used to denote directions (c) can be utilized to denote their direction relations, each ray corresponding to a cardinal direction (Yan et al., 2006) For example, in Fig 5, the directions from the river (A) to the road (B) may be expressed using a direction set Dir(A, B) = {NE, N, E} 3.4 Reasonability of using Voronoi diagram to express directions It is difficult to get a certain ray pointing from one object to another; however, the normals of the ray (i.e., the Voronoi diagram of the two objects) can be obtained Because a ray and its normal are perpendicular to each other, the ray can be obtained easily by its normals Figure presents the Voronoi diagrams and the ray between two point objects and between a point object and a linear object, respectively Obviously, each of the rays (normal of the Voronoi diagram) denotes the direction relations (d) Fig Procedures of of computing Fig.88 Procedures computing direction direction relations relations between between two two object object (a) generalized object (b) groups; (b) triangulation of groups; groups:groups: (a) generalized object groups; triangulation of the object the groups; (c)ofproximal sections the(d)object groups; and (c) object proximal sections the object groups;of and Voronoi Diagram (d) Voronoi diagram 4.2 Cartographic generalization of the two object groups According to “the relations between the sum of the whole and its parts”, cartographic generalization is a first necessary step in human’s direction judgments This procedure aims at simplifying object groups so that direction computation can be done in a simple way Suppose that the diameter of convex hull of the two object groups is d; Eq (1) is used to simplify spatial objects S = d × [1 − cos(ε/2)]/2 A Voronoi-based model To simplify the following discussion, the two object groups in Fig will be used as an example Here, river basin R is the reference object group; the village V is the target object group The eight-direction system (i.e., eight directions E, NE, N, NW, W, SW, S, and SE are discerned) will be employed Because both quantitative and qualitative direction relations are widely used in daily life, the proposed model will express direction relations in quantitative and qualitative ways 4.1 Framework of the model The new model for computing quantitative and direction relations consists of four procedures: cartographic generalization of the two object groups; construction of the Voronoi diagram; computation of quantitative direction relations; and construction of qualitative direction relations 33 www.geosci-model-dev.net/6/1591/2013/ (1) where S is the generalization scale of the objects (i.e., the details whose sizes are less than S will be simplified), and ε is an angle It equals 90◦ in the four-direction system and 45◦ in the eight-direction system The generalized result of Fig is shown in Fig 8a, which can be used for computing direction relations in the eightdirection system 4.3 Construction of the Voronoi diagram 34 It is well known that Delaunay triangulation is a useful and efficient tool in spatial adjacency/proximity analysis (Li et al., 2002); hence, it is used to get proximal sections of the two object groups On the other hand, the Delaunay triangular network and the Voronoi diagram are dual of each other (Arias et al., 2011); thus the Voronoi diagram of the two object groups can be easily obtained by their Delaunay triangular network The Voronoi diagram can be obtained by following steps First, construct a point set consisting of all of the vertices of the two object groups Second, construct the Delaunay triangular network (Fig 8b) of the point set If the three vertices of a triangle belong to one object group, it is called a “first-type triangle”; otherwise, it is called a “second-type triangle” Geosci Model Dev., 6, 1591–1599, 2013 1596 H Yan et al.: An approach to computing direction relations between separated object groups Table Quantitative description of direction relations from R to V in Fig x A Labeled edge Azimuth (degree) Weight (%) 82 133 205 237 11 20 26 16 27 α y O Fig.9 Definition of azimuth Fig Definition of azimuth Legend Next, delete all of the first-type triangles The remaining triangles compose the proximal area (Fig 8c) of the two groups Finally, generate the Voronoi diagram (Fig 8d) using the remaining triangles 4.4 Computation of quantitative direction relations Normal Fig 10 Simplified and labeled Voronoi edges with normals Fig.10 Simplified and labeled Table Qualitative description of direction relations from R to V Voronoi in Fig edges with normals The Voronoi diagram of two object groups generally consists of n ≥ Voronoi edges (e.g., the Voronoi diagram in Fig 8d has 15 edges); each Voronoi edge has a normal Hence, a total of n normals can be obtained to denote the direction pointing from the reference object group to the target object group In other words, there are n directions between the two object groups To describe direction relations quantitatively with the n directions, the following three strategies are employed Labeled edge – A single direction can be described using the azimuth of the normal of the Voronoi edge An azimuth of a ray is the angle measured clockwise from the positive end of the vertical axis of the Cartesian coordinate system to the ray Figure shows the azimuth (α) of ray O–A – To differentiate the importance of each direction, each direction is assigned a weight value, which is the percentage of the length of each corresponding Voronoi edge Because each Voronoi edge corresponds to a single direction, the Voronoi diagram may be generalized using Eq (1) as the criterion to simplify the final expression of the direction relations 4, Direction Weight (%) N E SE SW 11 20 26 16+27 = 43 quantitative direction relations of the two object groups Each direction consists of an angle and a weight value This quantitative result can be expressed as D(R, V ) = {< 1, 11 >, < 82, 20 >, < 133, 26 >, < 205, 16 >, < 237, 27 >} 4.5 Construction of qualitative direction relations To qualify the quantitative direction relations, the following two steps are needed – Change the azimuths into qualitative directions In the eight-direction system, north means an azimuth in [337.5◦ , 0◦ ]∪[0◦ , 22.5◦ ]; northwest an azimuth in [22.5◦ , 67.5◦ ]; east an azimuth in [67.5◦ , 112.5◦ ]; southeast an azimuth in [112.5◦ , 157.5◦ ]; south an azimuth in [157.5◦ , 202.5◦ ]; southwest an azimuth in [202.5◦ , 247.5◦ ]; west an azimuth in [247.5◦ , 292.5◦ ]; northwest an azimuth in [292.5◦ , 337.5◦ ] – To facilitate saving direction relations in databases, all of the azimuths and their corresponding weights are listed in a 2-dimensional table – Combine the same cardinal directions, and add up their corresponding weights The generalized Voronoi diagram in Fig 8d is shown in Fig 10 Its Voronoi edges are labeled Table presents the Table shows the qualitative description of direction relations from R to V in Fig The directions of edge and Geosci Model Dev., 6, 1591–1599, 2013 www.geosci-model-dev.net/6/1591/2013/ H Yan et al.: An approach to computing direction relations between separated object groups 1597 P Q (a) (b) (d) (e) (c) (f) Legend: Voronoi edge (g) (h) Fig 11 Examples of pairs of object groups of used in the ( A ) point → point (b) line →(a) point group; (c) polygon → point Fig.11 Examples pairs ofexperiment: object groups used in thegroup; experiment: point group; (d) line → line point network; (e) line → linear arranged polygon group; (f) polygon group → line network; (g) polygon cluster → linear group; (b) linepoint group; (c) polygonpoint group; (d) lineline arranged polygon group; (h) polygon → complex group with polygons, lines and points network; (e) linelinear arranged polygon group; (f) polygon groupline network; (g) polygon arranged polygon group; of(h) Table Qualitative direction relations of the pairsclusterlinear of object groups (the percentages are the weights thepolygon directions) complex group with polygons, lines and points Pair of groups N % NW % Fig 11a Fig 11b Fig 11c Fig 11d Fig 11e Fig 11f Fig 11g Fig 11h 73.67 26.82 19.34 50.07 5.03 34.44 16.17 12.94 11.48 49.05 10.90 49.93 13.82 5.66 5.74 W % 2.75 13.41 5.81 1.78 4.67 edge are the same (SW); hence, they are combined and their weights are added up This result can be Dir(R, V ) = {< N, 11 >, < E, 20 >, < SE, 26 >, < SE, 43 >} The qualitative description of direction relations in Fig is as follows: 11 % of V is to the north of R, 20 % of V to the east of R, 26 % of V to the southeast of R, and 43 % of V to the southwest of R Experiments and discussions Whether the proposed approach is correct and valid should be tested by psychological experiments, because judgments of directions are rooted in human’s spatial cognition (Egenhofer www.geosci-model-dev.net/6/1591/2013/ SW % S % SE % E % NE % 11.10 19.82 12.24 5.10 14.85 21.38 8.09 18.54 21.40 33.80 24.28 18.14 1.58 21.87 20.69 17.95 19.58 17.75 5.26 17.10 16.85 14.83 8.15 2.23 13.93 and Shariff, 1998; Gayal, 2000) For this purpose, the direction relations of 40 pairs of object groups were computed using a C# program implemented by the authors They were drawn in a table and distributed to 33 testees (all testees are graduates of Lanzhou Jiaotong University, China) The natural language description of direction relations was attached to each pair of object groups The testees were required to answer if they “totally agree”, “agree”, are “unsure”, or “do not agree” with each answer Figure 11 and Table give eight typical examples of our experiment The result of the psychological test is listed in Table Some insights can be gained from the experiments 37 Geosci Model Dev., 6, 1591–1599, 2013 1598 H Yan et al.: An approach to computing direction relations between separated object groups Table Statistical results of the psychological test (%) Pair of groups Fig 11a Fig 11b Fig 11c Fig 11d Fig 11e Fig 11f Fig 11g Fig 11h Mean research will focus on improving this approach so that it can be used to process topologically intersected and/or contained object groups Totally agree Agree Unsure Do not agree 70 30 67 67 67 48 67 39 56.9 24 34 27 27 27 36 27 48 31.2 24 6 16 10 9.3 12 Acknowledgements The work described in this paper is partially funded by the NSERC, Canada, partially funded by the National Support Plan in Science and Technology, China (No 2013BAB05B01), and partially funded by the Natural Science Foundation Committee, China (No 41371435) 3 2.6 Edited by: H Weller References First, Dir(B, A) can be obtained from Dir(A, B) by the proposed approach Taking Fig 11a as an example, a simple inversion of the three cardinal directions in Dir(Q, P ) = {< N, 73.67 >, < NW, 11.48 >, < NE, 14.85 >} can generate Dir(P , Q) = {< S, 73.67 >, < SE, 11.48 >, < SW, 14.85 >} Second, the mean of the confidence values from the test is 88.1 % (including “totally agree” and “agree”); the least is 64 %; the greatest is 94 % Hence, this approach is acceptable and valid from the point of view of spatial cognition Third, the proposed approach can be used to compute direction relations both between single objects and between object groups (Fig 11) Fourth, the results obtained by the approach are both quantitative (Table 4) and qualitative (Table 5) Moreover, the results are saved in 2-dimensional tables, facilitating the construction of databases for direction relations And finally, if two object groups are intersected, contained and/or covered with each other (i.e., they have common parts), the approach can not work well and needs to be improved Conclusions This paper proposed an approach to computing direction relations between two separated object groups in 2dimensional space The approach is supported by two principles in gestalt theory One is the principle of “the sum of the whole and its parts”, and the other one is the principle of proximity Its validity and soundness has been proved by psychological experiments The main advantages of this approach can be summarized as follows: (1) it can compute direction relations between object groups, which the other models can not; (2) it can obtain Dir(A, B) from Dir(B, A) without complex computation; (3) initial quantitative direction relations can be transformed into qualitative ones easily; and (4) quantitative and qualitative direction relations can be recorded in 2-dimensional tables, which is useful in spatial database construction and spatial reasoning Our further Geosci Model Dev., 6, 1591–1599, 2013 Abdelmoty, A I and Williams, M H.: Approaches to the representation of qualitative spatial relations for geographic databases, Geodesy, 40, 204–216, 1994 Alberto, G and Charles, S.: To 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Fig.88 Procedures computing direction direction relations relations between between two two object object (a) generalized object (b) groups; (b) triangulation of groups; groups: groups:... triangle” Geosci Model Dev., 6, 1591–1599, 2013 1596 H Yan et al.: An approach to computing direction relations between separated object groups Table Quantitative description of direction relations. ..1592 H Yan et al.: An approach to computing direction relations between separated object groups (a) (b) (c) (d) (e) (f) Explanation: the objects enclosed by dash-lined rectangle are viewed